中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人： 李彩燕 博士（北京大学）
题 目：Linearity of Homogeneous Order One Solutions to Elliptic Equations in Dimension Three
时 间：2021.12.16（星期四），14:00-15:30
地 点：思源楼S515
摘 要：I will report the work published on CPAM in 2003 by Han-Nadirashvili-Yuan. They proved that any homogeneous order one solution to nondivergence elliptic equations in R^3 must be linear. This result gives a simple PDE proof of a well-known result which states that any nonparametric minimal cone of dimension 3 must be flat. And it also implies that any smooth homogeneous order 2 solution in R^3\{0} to the fully nonlinear elliptic equation F(D^2u)=0 must be a quadratic polynomial.
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报告人： 李奇睿 教授（浙江大学）
题 目：A Monge-Ampere type functional and related prescribing curvature problems
时 间：2021.12.20（星期一），15:00-16:00
地 点：腾讯会议：298 673 475
摘 要：In this talk, we discuss the Minkowski problem in the sphere and the problem of prescribing the centro-affine curvature in the Euclidean space. The two problems are equivalent to solving the Euler-Lagrangian equations of a Monge-Ampere type functional in the sphere or Euclidean space. The solutions are obtained by using a Gauss curvature type flow together with min-max principle or some topological argument. The talk is based on recent joint work with Qiang Guang and Xu-Jia Wang.